Abstract. 

In a rectangular domain, a nonlocal boundary value problem is studied for the heat equation with a fractional Caputo derivative with variable coefficients. An a priori estimate in differential form is obtained by the method of energy inequalities. A difference scheme is constructed that approximates the boundary value problem with the first order. An analog of the a priori estimate in difference form is obtained. The obtained a priori estimates imply the uniqueness and stability of the solution with respect to the initial data and the righthand side. The convergence of the difference scheme to the solution of the original problem is proved.

Keywords: 

fractional Caputo derivative, boundary value problem, a priori estimate, difference scheme, method of energy inequalities, numerical methods.

DOI: 10.14357/20790279240201 

EDN: CAZNDM

PP. 3-10.

 

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